## Graph Theory, 1736-1936First published in 1976, this book has been widely acclaimed both for its significant contribution to the history of mathematics and for the way that it brings the subject alive. Building on a set of original writings from some of the founders of graph theory, the book traces the historicaldevelopment of the subject through a linking commentary. The relevant underlying mathematics is also explained, providing an original introduction to the subject for students. From reviews: 'The book...serves as an excellent examplein fact, as a modelof a new approach to one aspect of mathematics,when mathematics is considered as a living, vital and developing tradition.' (Edward A. Maziark in Isis) 'Biggs, Lloyd and Wilson's unusual and remarkable book traces the evolution and development of graph theory...Conceived in a very original manner and obviously written with devotion and a verygreat amount of painstaking historical research, it contains an exceptionally fine collection of source material, and to a graph theorist it is a treasure chest of fascinating historical information and curiosities with rich food for thought.' (Gabriel Dirac in Centaurus) 'The lucidity, grace andwit of the writing makes this book a pleasure to read and re-read.' (S. H. Hollingdale in Bulletin of the Institute of Mathematics and its Applications) |

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This book gives a self contained historical introduction to graph theory using thirty-seven extracts from original articles (translated when necessary).

### Contents

PATHS | 7 |

CIRCUITS | 21 |

TREES | 37 |

CHEMICAL GRAPHS | 55 |

EULERS POLYHEDRAL FORMULA | 74 |

THE FOURCOLOUR PROBLEM | 90 |

COLOURING MAPS ON SURFACES | 109 |

THE FOURCOLOUR PROBLEMTO 1936 | 158 |

THE FACTORIZATION OF GRAPHS | 187 |

Graph Theory since 1936 | 209 |

Bihliography 17361936 | 223 |

235 | |

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### Common terms and phrases

1-cells 1-circuit ahout ahove ahstract algehra arhitrary assemhlage Birkhoff Cayley chapter chromatic polynomials circuit colours connected pieces contains corresponding degree denoted hy descrihe diagram districts dual equations Euler Euler's formula Eulerian path example follows formula four four-colour conjecture four-colour prohlem G. D. BIRKHOFF geometry given graph theory Heawood hecame hecause hecome heen hefore hegin helong hetween hexagons hinary hlue hook hoth houndary hranches hridges leading irreducihle map joined Kirkman knight's tour knots Konigsherg lahels letter Lhuilier lines Math mathematical mathematician Mohius neighhouring regions node nullity numher of edges numher of hridges numher of vertices odd numher paper path pentagons Petersen's planar graphs plane point of concourse polygon polyhedra polyhedron possihle proof proved puhlished regular graph represented hy result solution sphere suhgraph suhject Sylvester symhol theorem topology total numher traversed trees triangles trivalent trivalent graph valency variahles vertex W. T. Tutte